Câu 1: So sánh P và Q:
P = 2016/2017 + 2017/2018 + 2018/2019
Q = 2016+2017+2018/2017+2018+2019.
Câu 2: Tìm x:
( 2,7x – 1 1/2x ) : 2/7 = -21/4
( 1 1/2 là hỗn số nhân vs x nha, 2,7 là số thập phân )
Câu 1: So sánh P và Q:
P = 2016/2017 + 2017/2018 + 2018/2019
Q = 2016+2017+2018/2017+2018+2019.
Câu 2: Tìm x:
( 2,7x – 1 1/2x ) : 2/7 = -21/4
( 1 1/2 là hỗn số nhân vs x nha, 2,7 là số thập phân )
Câu 1:
Ta có:
` P = 2016/2017 + 2017/2018 + 2018/2019 `
` <=> P = \frac{2016}{2017 + 2018 + 2019} + \frac{2017}{2018 + 2017 + 2019} + \frac{2018}{2019 + 2017 + 2018} `
Vì ` \frac{2016}{2017+2018+2019} > \frac{2016+2017+2018}{2017+2018+2019} `
` \frac{2017}{2017+2018+2019} > \frac{2016+2017+2018}{2017+2018+2019} `
` \frac{2018}{2017+2018+2019} > \frac{2016+2017+2018}{2017+2018+2019} `
` => \frac{2016}{2017 + 2018 + 2019} + \frac{2017}{2018 + 2017 + 2019} + \frac{2018}{2019 + 2017 + 2018} > \frac{2016+2017+2018}{2017+2018+2019} `
` => P > Q `
Câu 2:
` (2,7x – 1 1/2 x) : 2/7 = -21/4 `
` => 27/10 x – 3/2 x = -21/4 . 2/7 `
` => 6/5 x = -3/2 `
` => x = -3/2 . 5/6 `
` => x = -5/4 `
Đáp án:
$1) P>Q$
$2)
x=\dfrac{-5}{4}$
Giải thích các bước giải:
$1)P=\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}\\
Q=\dfrac{2016+2017+2018}{2017+2018+2019}\\
=\dfrac{2016}{2017+2018+2019}+\dfrac{2017}{2017+2018+2019}+\dfrac{2018}{2017+2018+2019}\\$
Do $2017<2017+2018+2019$
$\Rightarrow \dfrac{2016}{2017}>\dfrac{2016}{2017+2018+2019}(1)\\
2018<2017+2018+2019\\
\Rightarrow \dfrac{2017}{2018}>\dfrac{2017}{2017+2018+2019}(2)\\
2019<2017+2018+2019\\
\Rightarrow \dfrac{2018}{2019}>\dfrac{2018}{2017+2018+2019}(3)\\
(1),(2),(3)\Rightarrow \dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}>\dfrac{2016}{2017+2018+2019}+\dfrac{2017}{2017+2018+2019}+\dfrac{2018}{2017+2018+2019}\\
\Leftrightarrow P>Q$
$2)
(2,7x-1\dfrac{1}{2}x):\dfrac{2}{7}=\dfrac{-21}{4}\\
\Leftrightarrow \left ( \dfrac{27}{10}-\dfrac{3}{2} \right )x.\dfrac{7}{2}=\dfrac{-21}{4}\\
\Leftrightarrow \left ( \dfrac{27}{10}-\dfrac{15}{10} \right )x.\dfrac{7}{2}=\dfrac{-21}{4}\\
\Leftrightarrow \dfrac{12}{10}x.\dfrac{7}{2}=\dfrac{-21}{4}\\
\Leftrightarrow \dfrac{21}{5}x=\dfrac{-21}{4}\\
\Leftrightarrow x=\dfrac{-21}{4}.\dfrac{5}{21}\\
\Leftrightarrow x=\dfrac{-5}{4}$